Global existence, asymptotic stability and blow‐up of solutions for the generalized Boussinesq equation with nonlinear boundary condition

Abstract

AbstractIn this paper, we consider initial boundary value problem of the generalized Boussinesq equation with nonlinear interior source and boundary absorptive terms. We establish firstly the local existence of solutions by standard Galerkin method. Then we prove both the global existence of the solution and a general decay of the energy functions under some restrictions on the initial data. We also prove a blow‐up result for solutions with positive and negative initial energy respectively.